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The numerical interface coupling of nonlinear hyperbolic systems of conservation laws. I: The scalar case. (English) Zbl 1063.65080
This work is devoted to the theoretical and numerical coupling of two general hyperbolic conservation laws. The coupling preserves in a weak sense the continuity of the solution at the interface without imposing the overall conservativity of the coupled model. The authors prove the convergence and characterize the limit solution of the coupled schemes in a few simple but significative coupling situations. The general coupling problem is analyzed for Riemann initial data. Numerical experiments are presented.

MSC:
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
35L65 Hyperbolic conservation laws
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
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